If you do naive matrix multiplication, you get a sense that you're doing similar work multiple times, but it's hard to quantify just what that duplicated work entails. Compare it to, for example, calculating the size of the union of two sets:

Total size = size(A) + size(B) - size(intersection(A, B))

You have to take out that extra intersection amount because you've counted it twice. What if you could avoid counting it twice in the first place? That's easy, you just iterate over each set once, keeping track of the elements you've already seen.

Strassen's algorithm keeps track of calculations that are needed later on. It's all reminiscent of dynamic programming.

What I find interesting is that it seems the extra savings requires complex values. There must be something going on in the complex plane that is again over-counting with the naive approach.

On the other side, it's claimed here that an algorithm that uses only 46 multiplications has been known since 1970: https://mathstodon.xyz/@fredrikj/114508287537669113

Edit2: Z_2 has characteristics 2.

Edit: AlphaEvolve claims it works over any field with characteristic 0. It appears Waksman's could be an existing work. From the AlphaEvolve paper: "For 56 years, designing an algorithm with fewer than 49 multiplications over any field with characteristic 0 was an open problem. AlphaEvolve is the first method to find an algorithm to multiply two 4 × 4 complex-valued matrices using 48 multiplications."

1. It is a standard example of the divide and conquer approach to algorithm design, not the dynamic programming approach. (I'm not even sure how you'd squint at it to convert it into a dynamic programming problem.)

2. Strassen's does not require complex valued matrices. Everything can be done in the real numbers.

In other words, the power of Strasssens algorithm comes from a strategy that's similar to / reminiscent of dynamic programming.

> In roughly 75% of cases, it rediscovered state-of-the-art solutions, to the best of our knowledge.

> And in 20% of cases, AlphaEvolve improved the previously best known solutions

These sound like incredible results. I'd be curious what kind of improvements were made / what the improvements were.

Like, was that "up to a 32.5% speedup" on some weird edge case and it was negligible speed up otherwise? Would love to see the benchmarks.

It's a very impressive result, but not magic, but also not cheating!

Previously we needed to have a human in the loop to do the change. Of course we have automated hyperparameter tuning (and similar things), but that only works only in a rigidly defined search space.

Will we see LLMs generating new improved LLM architectures, now fully incomprehensible to humans?

Edit the white paper says this: AlphaEvolve employs an ensemble of large language models. Specifically, we utilize a combination of Gemini 2.0 Flash and Gemini 2.0 Pro. This ensemble approach allows us to balance computational throughput with the quality of generated solutions. Gemini 2.0 Flash, with its lower latency, enables a higher rate of candidate generation, increasing the number of ideas explored per unit of time. Concurrently, Gemini 2.0 Pro, possessing greater capabilities, provides occasional, higher-quality suggestions that can significantly advance the evolutionary search and potentially lead to breakthroughs. This strategic mix optimizes the overall discovery process by maximizing the volume of evaluated ideas while retaining the potential for substantial improvements driven by the more powerful model.

So, I remain of my opinion before. Furthermore, in the paper they don't present it as something extraordinary as some people here say it is, but as an evolution of another existing software, funsearch

The last 50 years of software evolution have been driven by a need to scale human comprehension for larger and more integrated codebases. If we decreasingly need/rely on humans to understand our code, source code’s forward-progress flywheel is going to slow down and will bring us closer to (as you suggest) incomprehensibility.

Not only did we scale the breadth of codebases - the flywheel built layers and layers of abstraction over time (have you seen the code sample in this article??), fostering a growing market of professional developers and their career progressions; if most code becomes incomprehensible, itll be the code closer to “the bottom”, a thin wrapper of API on top of an expanding mass of throwaway whatever-language AlphaAlgo creates.

If we don’t wrangle this, it will destroy a profession and leave us with trillions of LoC that only people with GPUs can understand. Which may be another profession I suppose.

FA achieving a 32.5% speed up? Cool.

Why not submit it as a PR to the Flash Attention repo then? Can I read about it more in detail?

""" Yesterday's news about Sakana AI Labs provided an important lesson for all of us working with AI agents. Their announcement of an AI system that could supposedly optimize CUDA kernels to run 100x faster initially seemed like exactly the kind of use cases we've been hoping for in AI-assisted development.

Like many others, I was excited about it. After all, isn't this exactly what we want AI to do - help us optimize and improve our technical systems?

However, careful investigation by the community (on Twitter) revealed a different story. What really happened? The AI-generated CUDA kernel appeared to achieve incredible speedups, but the code was inadvertently reusing memory buffers containing previous results, essentially bypassing the actual computation. When properly evaluated, the kernel actually runs about 3x slower than the baseline. """

[1] https://www.linkedin.com/posts/ravid-shwartz-ziv-8bb18761_ye...

[2] https://x.com/main_horse/status/1892473238036631908

I’ve seen it so much I kinda doubt it was “inadvertent” because they’re like seemingly intentional about their laziness, and will gaslight you about it too.

Funny, 5 years ago we had these same complaints, but about (some) people.

But how incremental are these advancements?

I picked one at random (B.2 -- the second autocorrelation inequality). Then, I looked up the paper that produced the previous state of the art (https://arxiv.org/pdf/0907.1379). It turns out that the authors had themselves found the upper bound by performing a numerical search using "Mathematica 6" (p.4). Not only did the authors consider this as a secondary contribution (p.2), but they also argued that finding something better was very doable, but not worth the pain:

"We remark that all this could be done rigorously, but one needs to control the error arising from the discretization, and the sheer documentation of it is simply not worth the effort, in view of the minimal gain." (p.5)

So at least in this case it looks like the advancement produced by AlphaEvolve was quite incremental (still cool!).

This is complex automation which by definition compresses the solution into a computable process that works more efficiently than the non-automated process

That, in fact, is the revolutionary part - you’re changing how energy is used to solve the problem.

Like even just for programming. I just had an AI instrument my app for tracing, something I wanted to do for a while, but I didn't know how to do and didn't feel like figuring out how to do it. That's not work we were likely to hire someone to do or that would ever get done if the AI wasn't there. It's a small thing, but small things add up.

In a way it is nothing new but natural progression of technology. It is increasing pace of change that is different. Can a person learn some skills by their 20s and apply productively throughout their lifetime? Now at this point it is so thoroughly untrue that I'd be laughed out if I asked for such thing. We are told to up skill few times in career to up-skilling continuously.

As changes are getting faster and faster more people are gonna fall wayside and of course they can blame themselves for their predicament.

Automation changed farming for the worse? Farmers today are not respected / valued for their work? Farmers were replaced with low skilled labor? Do you think the job of a farmer (aka "food grower") will stop existing?

I do not predict future only look at what happened in the past and my answer to each question above about farming is the opposite what your comment would imply if it was applied to farming.

Farmers couldn't be replaced by low skill labor because they are low skill.

Farmer didn't stop existing, but we went from 80% of the population farming is to 1-10%. If farming automation had happened in 1800 when 80% of the workforce was working in agriculture, it'd have been a cataclysm.

I'm pretty sure there is a slight widespread lack of respect for software engineers, mainly offset by their high salaries. Wait and see once vibecoding becomes the new norm.

And for software engineers, yeah, automation will wreck their jobs and their paychecks because software engineering's higher speed limit in efficiency is the speed of light, not a tractor's.

I can list lot more jobs e.g exchange admins, app server admins, DBAs, they are either gone or far fewer available. And lot of people were not able to up-skill and fell out of race in just a matter of 15-20 years.

Pretty much most of them feel underpaid for the amount of hard work and I hear they're having problem recruiting younger people to the business, so many foreigners take those jobs.

Of course my life is bit better as I saved few hours on weekend as owner of house and a vacuum cleaner.

But my life as worker is worse in last 10 years as knowledge of developing large complex applications is not valuable because we are in Next Gen Cloud native era where one application will not contain more than 5 functions anyway. Even if I claim I can write better maintainable, performance code , the employer directly or indirectly says "Well we don't care, we need you to complete these 10 JIRAs in this sprint" And only answer they take from me is yes.

LLMs are undoubtedly useful at tasks like code "optimisation" and detecting patterns or redundancies that humans might overlook, but this announcement feels like another polished, hypey blog post from Google.

What's also becoming increasingly confusing is their use of the "Alpha" branding. Originally, it was for breakthroughs like AlphaGo or AlphaFold, where there was a clear leap in performance and methodology. Now it's being applied to systems that, while sophisticated, don't really rise to the same level of impact.

edit: I missed the evaluator in my description, but an evaluation method is applied also in Co-Scientist:

"The AI co-scientist leverages test-time compute scaling to iteratively reason, evolve, and improve outputs. Key reasoning steps include self-play–based scientific debate for novel hypothesis generation, ranking tournaments for hypothesis comparison, and an "evolution" process for quality improvement."[0]

[0]: https://research.google/blog/accelerating-scientific-breakth...

"While AI Co-Scientist represents scientific hypotheses and their evaluation criteria in natural language, AlphaEvolve focuses on evolving code, and directs evolution using programmatic evaluation functions. This choice enables us to substantially sidestep LLM hallucinations, which allows AlphaEvolve to carry on the evolution process for a large number of time steps."

For example, for self driving, it makes much more sense to treat it like a game, where the model learns the evolution of the surrounding environment, and learns how its own actions affect it, and can MCTS its way into correct behavior - specifically because once it learns the environment dynamics, it can internally simulate crashes and retrain itself.

If this process is refined (namely the functions that control direction of training) , you can pretty much start training a model on the dataset of real world (sights, sounds, physical interactions, as well as digital ones), and as it learns the environment, it can be further and further refined, and then we get to the point where it can self evolve its decision making to be truly considered "intelligent".

https://research.google/blog/accelerating-scientific-breakth...

Some related work from a different company: https://sakana.ai/ai-cuda-engineer/

And some academic papers kind of in this space: https://arxiv.org/abs/2206.08896, https://arxiv.org/abs/2302.12170, https://arxiv.org/abs/2401.07102

On the other side I see excitement that the singularity is here.

If the latter were the case surely we wouldn't be reading about it in a published paper, we would already know.

[1] Blog: https://deepmind.google/discover/blog/discovering-novel-algo...

[2] Paper: https://www.nature.com/articles/s41586-022-05172-4

[3] arxiv.org/pdf/2210.04045

[4] arxiv.org/abs/2212.01175 Flip graphs for matrix multiplication

(Reposted from here, where I made a mini deep-dive into this: https://x.com/friederrrr/status/1922846803420119410?t=7jZ34P...)

I don't know if I would call this the fabled "self improving feedback loop", but it seems to have some degree of it. It also begs the question if Alphaevolve was being developed for a year, or has been in production for a year. By now it makes sense to hold back on sharing what AI research gems you have discovered.

In the specific context of improving our AI hardware, for example, it's not as simple as coming up with a good idea -- hardware companies hire thousands of people to improve their designs. Prototypes need to be implemented, verified, quantified, compared thoroughly with the alternatives, then the idea is approved for production, which again leads to a cascade of implementation, verification, etc. until they can reach consumers. In order to make these improvements reach the consumer significantly faster you need to accelerate all of the steps of the very simplified pipeline mentioned earlier.

More generally, an argument can be made that we have been in that take off feedback loop for hundreds of years; it's just that the rate of improvement hasn't been as spectacular as we may have hoped for because each incremental step simply isn't that big of a deal and it takes quite a bit of time to reach the next one.

"DeepMind AI Reduces Google Data Centre Cooling Bill by 40%"

https://deepmind.google/discover/blog/deepmind-ai-reduces-go...

The use of synthetic data from prior models to create both superior models and distilled models has been going on since at least OpenAI's introduction of RLHF, and probably before that too.

That’s distinct from those prior models providing actual code to improve the next model

> By suggesting modifications in the standard language of chip designers, AlphaEvolve promotes a collaborative approach between AI and hardware engineers to accelerate the design of future specialized chips."

> AlphaEvolve was able to find a simple code rewrite (within an arithmetic unit within the matmul unit) that removed unnecessary bits, a change validated by TPU designers for correctness.

I speculate this could refer to the upper bits in the output of a MAC circuit being unused in a downstream connection (perhaps to an accumulation register). It could also involve unused bits in a specialized MAC circuit for a non-standard datatype.

> While this specific improvement was also independently caught by downstream synthesis tools, AlphaEvolve’s contribution at the RTL stage demonstrates its capability to refine source RTL and provide optimizations early in the design flow.

As the authors admit, this bit-level optimization was automatically performed by the synthesis tool (the equivalent to this in the software-world is dead code elimination being performed by a compiler). They seem to claim it is better to perform this bit-truncation explicitly in the source RTL rather than letting synthesis handle it. I find this dubious since synthesis guarantees that the optimizations it performs do not change the semantics of the circuit, while making a change in the source RTL could change the semantics (vs the original source RTL) and requires human intervention to check semantic equivalence. The exception to this is when certain optimizations rely on assumptions of the values that are seen within the circuit at runtime: synthesis will assume the most conservative situation where all circuit inputs are arbitrary.

I do agree that this reveals a deficiency in existing synthesis flows being unable to backannotate the source RTL with the specific lines/bits that were stripped out in the final netlist so humans can check whether synthesis did indeed perform an expected optimization.

> This early exploration demonstrates a novel approach where LLM-powered code evolution assists in hardware design, potentially reducing time to market.

I think they are vastly overselling what AlphaEvolve was able to achieve. That isn't to say anything about the potential utility of LLMs for RTL design or optimization.

Cf. the second paragraph of 3.3.4 of https://storage.googleapis.com/deepmind-media/DeepMind.com/B...

You can't write an evaluation function for general "intelligence"...

> AlphaEvolve enhanced the efficiency of Google's data centers, chip design and AI training processes — *including training the large language models underlying AlphaEvolve itself*.

Singularity people have been talking for decades about AI improving itself better than humans could, and how that results in runaway compounding growth of superintelligence, and now it's here.

If it takes you a week to find a 1% speedup, and the next 0.7% speedup takes you 2 weeks to find ... well, by using the 1% speedup the next one only takes you 13.86 days. This kind of small optimization doesn't lead to exponential gains.

That doesn't mean it's not worthwhile - it's great to save power & money and reduce iteration time by a small amount. And it combines with other optimizations over time. But this is in no way an example of the kind of thing that the singularity folks envisioned, regardless of the realism of their vision or not.

It optimized

   initializers.normal (0.0

   initializers.normal (0 + 1j * 0,

Anyway, impressive results. That's why OpenAI and Elon were so frightened about Hassabi.

>In AlphaEvolve, the evolutionary database implements an algorithm that is inspired by a combination of the MAP elites algorithm [71] and island-based population models [80, 94].

"inspired by" is doing a lot of heavy lifting in this sentence. How do you choose dimensions of variation to do MAP-elites? How do you combine these two algorithms? How loose is the inspiration? It feels like a lot of the secret sauce is in the answers to these questions, and we get a single paragraph on how the evolution procedure works, which is so vague as to tell us almost nothing.

Agreed the dimensions/features are key. These white papers are an insult to science...

If it goes well, I could open source it.

What are the things you would want to optimize with such a framework? (So far I've been focusing on optimizing ML training and architecture search itself). Hearing other ideas would help motivate me to open source if there's real demand for something like this.

In my case, I'd mainly be interested in mathematics: I'd provide a mathematical problem and a baseline algorithm for it and would want an open source framework to be able to improve on that.

Had mentioned the same on X: https://x.com/friederrrr/status/1922850981181784152?t=usXpK1...

Philosophically, let's say you talk an old LLM through a new discovery. Thanks to your instruction, the LLM now has access to "new" information not in its training data. It is certainly capable of this. The problem in is that this is just laundered human intelligence.

As a corollary, once you add in self-play with random variation, the synthetic data problem is solved for coding, math, and some classes of scientific reasoning. No more modal collapse, no more massive teams of PhDs needed for human labeling, as long as you have a reliable metric for answer quality.

This isn't just neat, it's important - as we run out of useful human-generated data, RL scaling is the best candidate to take over where pretraining left off.

I guess that's now becoming true with LLMs.

Faster LLMs -> More intelligence

couldn't you say that if you squint hard enough, GA looks like a category of RL? There are certainly a lot of similarities, the main difference being how each new population of solutions is generated. Would not at all be surprised that they're using a GA/RL hybrid.

Gradient descent is literally following the negative of the gradient to minimize a function. It requires a continuous domain, either analytical or numerical derivatives of the cost function, and has well-known issues in narrow valleys and other complex landscapes.

It’s also a local minimization technique and cannot escape local minima by itself.

_Stochastic_ gradient descent and related techniques can overcome some of these difficulties, but are still more or less local minimization techniques and require differentiable and continuous scoring functions.

In contrast, genetic algorithms try to find global minima, do not require differentiable scoring functions, and can operate on both continuous and discrete domains. They have their own disadvantages.

Different techniques for different problems. The field of numerical optimization is vast and ancient for a reason.

They are having some success in making it work internally. Maybe only the team that built it can get it to work? But it does seem promising.

As far as I can read, the weights of the LLM are not modified. They do some kind of candidate selection via evolutionary algorithms for the LLM prompt, which the LLM then remixes. This process then iterates like a typical evolutionary algorithm.

I suppose you could consider that last part (optimizing some metric) "RL".

However, it's missing a key concept of RL which is the exploration/exploitation tradeoff.

Not saying it is that egregious, but it's a slippery slope from "well, it didn't do all these different things out of the box, unsupervised".

They have other models with different names used for different purposes.

https://ai.google/get-started/our-models/

...but Waksman's algorithm from 1970 [1] multiplies two 4 x 4 complex-valued matrices using only 46 multiplications (indeed, it works in any ring admitting division by 2).

Sloppy by DeepMind and by Nature to publish such a claim - did they not ask someone knowledgeable about matrix multiplication to review the work?

[1] https://doi.org/10.1109/T-C.1970.222926

1. Waksman's algorithm works in any commutative ring admitting division by 2.

2. In particular, it won't work when the matrix entries are themselves matrices, which means you can't use it recursively to get an algorithm for n-by-n matrices with large n with a better exponent than you get from Strassen's algorithm.

3. The Deep Mind paper is annoyingly unexplicit about whether the algorithm it reports has that property or not.

4. What they say about tensors suggests that their algorithm can be used recursively to do better than Strassen (but, note, there are other algorithms that are substantially better for very large n which using their algorithm recursively would very much not outperform) but it's possible I've misunderstood.

5. They explicitly talk about complex-valued matrices, but I think they don't mean "complex numbers as opposed to matrices, so you can't do this recursively" but "complex numbers as opposed to real numbers, so our algorithm doesn't get you a 4x4 matmul using 48 real multiplications".

I am not certain about points 4 and 5. The language in the paper is a bit vague. There may be supporting material with more details but I haven't looked.

2. Correct, however you can use Waksman as a basecase and always beat Strassen (though it is not asymptotically better of course).

5. Possible, but even so, there is already an algorithm that will work with 46 real multiplications (and some divisions by 2). The real numbers are commutative and admit division by 2.

In 1996, they optimized an FPGA using a genetic algorithm. It evolved gates disconnected from the circuit, but were required.

The circuit exploited the minuscule magnetic fields from the disconnected gates rather than the logical connections.

[0] https://en.wikipedia.org/wiki/Evolvable_hardware

Is this basically a merge of LLM's with genetic algorithm iteration?

Anybody knows how they can guarantee uniqueness of searched snipped within code block or is it even possible?

- One lesson DeepMind drew from AlphaCode, AlphaTensor, and AlphaChip is that large‑scale pre‑training, combined with carefully chosen inductive biases, enables models to solve specialized problems at—or above—human performance.

- These systems still require curated datasets and experts who can hand‑design task‑specific pipelines.

- Conceptually, this work is an improved version of FunSearch (https://github.com/google-deepmind/funsearch/).

- In broad terms, FunSearch (and AlphaEvolve) follow three core design principles:

    - Off‑the‑shelf LLMs can both generate code and recall domain knowledge. The “knowledge retrieval” stage may hallucinate, but—because the knowledge is expressed as code—we can execute it and validate the result against a custom evaluation function.

    - Gradient descent is not an option for discrete code; a zeroth‑order optimizer—specifically evolutionary search—is required.

    - During evolution we bias toward (1) _succinct_ programs and (2) _novel_ programs. Succinctness is approximated by program length; novelty is encouraged via a MAP‑Elites–style “novelty bias,” yielding a three‑dimensional Pareto frontier whose axes are _performance, simplicity,_ and _novelty_ (see e.g. OE‑Dreamer: (https://claireaoi.github.io/OE-Dreamer/).

- Any general‑purpose foundation model can be coupled with evolutionary search.

- A domain expert merely supplies a Python evaluation function (with a docstring explaining domain‑specific details). Most scientists I've talked with - astronomers, seismologists, neuroscientists, etc. - already maintain such evaluation functions for their own code.

- The output is an interpretable program; even if it overfits or ignores a corner case, it often provides valuable insight into the regimes where it succeeds.

Cons

- Evolutionary search is compute‑heavy and LLM calls are slow unless heavily optimized. In my projects we need ≈ 60 k LLM calls per iteration to support a reasonable number of islands and populations. In equation discovery we offset cost by making ~99 % of mutations purely random; every extra 1 % of LLM‑generated mutations yields roughly a 10 % increase in high‑performing programs across the population.

- Evaluation functions typically undergo many refinement cycles; without careful curation the search may converge to a useless program that exploits loopholes in the metric.

Additional heuristics make the search practical. If your evaluator is slow, overlap it with LLM calls. To foster diversity, try dissimilar training: run models trained on different data subsets and let them compete. Interestingly, a smaller model (e.g., Llama-3 8 B) often outperforms a larger one (Llama‑3 70 B) simply because it emits shorter programs.

1. Why does it need a zeroth order optimizer?

2. Most GA's I've seen use thousands of solutions. Sometimes ten thousand or more. What leads you to use 60,000 calls per iteration?

3. How do you use populations and "islands?" I never studied using islands.

4. You said the smaller models are often better for "shorter" code. That makes sense. I've seen people extend the context of model with training passes. You think it would help to similarly shrink a larger model to a smaller context instead of using the small models?

Can you give a concrete example of this? It's hard for me to conceptualize.

Nowadays it makes much more sense to share less.

I honestly have no idea how AlphaEvolve works - does it work purely on the text level? Meaning I might be able to come up with something like AlphaEvolve with some EC2's and a Gemini API access?

[1]: https://arxiv.org/html/2505.05896v1

Just wait until the MBA's and politicians learn about this Adam Smith guy. A pipedream now, but maybe in the future schools will be inspired to teach about dialectical reasoning and rediscover Socrates.

[end of snark]

Sorry, I'm getting tired of ad-fueled corporations trying to get me to outsource critical thinking.

I'm reading descriptions of agents and it just seems like the same tech deployed with authority to write and a scheduler

Similar to hiring good students from famous universities even if most of CS isn't that applicable to day to day programming work, just because it's a signal that they're smart and managed to get through a difficult course.

Remember this approach only works for exploring an optimization for an already defined behavior of a function which has an accordingly well defined evaluation metric.

You can't write an evaluation function for each individual piece of or general "intelligence"...

Either way, it's pretty wild.

Packing problems are hard, and it is fun to see new interest in the area given these show up in weird places. =3

Some of these questions change slightly, since we might end up with "unlimited resources" (i.e. instead of having e.g. 5 engineers on a team who can only get X done per sprint, we effectively have near-limitless compute to use instead) so maybe the answer is "build everything on the wish-list in 1 day" to the "what should we prioritize" type questions?

Interesting times.

My gut is that software engineers will end up as glorified test engineers, coming up with test cases (even if not actually writing the code) and asking the AI to write code until it passes.

> about: I believe in the creation of a machine god

Sounds about right.

Not necessarily. 'Gospel' is translated as good news. The unpleasant news tends towards those within the power structure that the prophet challenges.

That isn't every problem in software engineering.

If the cost of developing the software is 0, you can just build both.

I'm now no longer surprised just how consistently all the gemini models overcomplicate coding challenges or just plain get them wrong.

Claude is just consistently spot on. A few salient comments for tricky code instead of incessantly telling me what it's changed and what I might want to do, incorrect assumptions when it has the code or is something we've discussed, changing large amounts of unrelated code (eg styles). I could go on.

Shame I'm too tight to pay for Claude RN though...

You can try asking it to not do that, but I would bet it would slightly degrade code quality.

You can take the code and give it to another LLM instance and ask it to strip all comments.